Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 9, 2005–2264
Issue 8, 1777–2003
Issue 7, 1547–1776
Issue 6, 1327–1546
Issue 5, 1025–1326
Issue 4, 777–1024
Issue 3, 521–775
Issue 2, 231–519
Issue 1, 1–230

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
The F-rational signature and drops in the Hilbert–Kunz multiplicity

Melvin Hochster and Yongwei Yao

Vol. 16 (2022), No. 8, 1777–1809
Abstract

Let (R,𝔪) be a Noetherian local ring of prime characteristic p. We define the F-rational signature of R, denoted by r (R), as the infimum, taken over pairs of ideals I J such that I is generated by a system of parameters and J is a strictly larger ideal, of the drops e HK (I,R)) e HK (J,R) in the Hilbert–Kunz multiplicity. If R is excellent, then R is F-rational if and only if r (R) > 0. The proof of this fact depends on the following result in the sequel: Given an 𝔪-primary ideal I in R, there exists a positive δI + such that, for any ideal J I, e HK (I,R) e HK (J,R) is either 0 or at least δI. We study how the F-rational signature behaves under deformation, flat local ring extension, and localization.

Keywords
F-rational signature, F-signature, Hilbert–Kunz multiplicity, Frobenius, Cohen–Macaulay, Gorenstein, regular
Mathematical Subject Classification 2010
Primary: 13A35
Secondary: 13C13, 13H10
Milestones
Received: 19 September 2017
Revised: 8 August 2021
Accepted: 22 November 2021
Published: 29 November 2022
Authors
Melvin Hochster
Department of Mathematics
University of Michigan
Ann Arbor
MI
United States
Yongwei Yao
Department of Mathemaics and Statistics
Georgia State University
Atlanta
GA
United States